Minimal Lagrangian and Product Geometries

This theme concerns minimal Lagrangian surfaces and related surface theories in complex space forms, para-complex spaces, quadrics, and product geometries.

Topics

• Minimal Lagrangian surfaces in complex projective and hyperbolic spaces.
• Ruh--Vilms type theorems.
• Loop group methods for quadrics and para-complex projective spaces.
• Willmore surfaces in product spaces.

Representative publications

• Ruh-Vilms theorems for minimal surfaces without complex points and minimal Lagrangian surfaces in CP^2.
• Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space.
• Minimal Lagrangian surfaces in the two dimensional complex quadric via the loop group method.